Opposite angles formed by an intersection of two lines.
Now, let's consider the given diagram.
To determine a pair of adjacent angles, let's take a look at the given diagram, looking for a pair of angles that share a vertex and a common side.
Looking at the diagram, ∠ FAE and ∠ EAD share A as a vertex and AE as a side. Therefore, these angles are adjacent. Now, let's look for a pair of angles whose measures sum to 90^(∘) — a pair of complementary angles.
Looking at the markings on the given diagram, we see that ∠ EAD, ∠ DAC, and ∠ CAB are adjacent angles that sum to the straight angle ∠ BAE. The measures of these angles sum to 180^(∘). Moreover, ∠ DAC is a right angle, so it measures 90^(∘). Therefore, we can write the following equation.
m∠ EAD + 90^(∘) + m∠ CAB = 180^(∘)
We can subtract 90^(∘) from both sides of this equation to get the sum of measures of m∠ EAD and m∠ CAB.
m∠ EAD + m∠ CAB = 90^(∘)
Since the sum of these measures is 90^(∘), these angles are complementary. Now, let's look for a pair of angles that sum to 180^(∘) — a pair of supplementary angles.
Looking at the markings on the given diagram, ∠ EAC and ∠ CAB sum to the straight angle ∠ EAB. Therefore, the sum of the measures of these angles is the measure of ∠ EAB — 180^(∘). As a result, ∠ EAC and ∠ CAB are supplementary. Finally, let's look for a pair of vertical angles. These angles are on the opposite sides of an intersection of two lines.
Looking at the diagram, there are no two lines that cross, so there are no vertical angles.
